.. automodule:: mapper.filters :members: .. function:: eccentricity(data, exponent=1.0, metricpar={}, callback=None) The eccentricity filter is the higher the further away a point is from the â€˜centerâ€™ of the data. Note however that neither an explicit central point is required nor a barycenter in an embedding of the data. Instead, an intrinsic notion of centrality is derived from the pairwise distances. If *exponent* is finite: .. math:: \mathit{eccentricity}(i)=\left(\frac 1N\sum_{j=0}^{N-1} d(x_i,x_j)^{\mathit{exponent}}\right)^{1/\mathit{exponent}} If *exponent* is numpy.inf: .. math:: \mathit{eccentricity}(i)=\max_j d(x_i,x_j) This is an equivalent description: Consider the full :math:(N\times N)-matrix of pairwise distances. The eccentricity of the :math:i-th data point is the Minkowski norm of the :math:i-th row with the respective *exponent*. .. function:: Gauss_density(data, sigma, metricpar={}, callback=None) Kernel density estimator with a multivariate, radially symmetric Gaussian kernel. For vector data and :math:x\in\mathbb{R}^d: .. math:: \mathit{Gauss\_density}(x) = \frac{1}{N(\sqrt{2\pi}\sigma)^d} \sum_{j=0}^{N-1}\exp\left(-\frac{\|x-x_j\|^2}{2\sigma^2}\right) The density estimator is normalized to a probability measure, i.e. the integral of this function over :math:\mathbb{R}^d is 1. The :math:i-th filter value is the density estimator evaluated at :math:x_i. For dissimilarity data: .. math:: \mathit{Gauss\_density}(i) = \sum_{j=0}^{N-1}\exp\left(-\frac{d(x_i,x_j)^2}{2\sigma^2}\right) In this case, the density estimator is not normalized since there is no domain to integrate over.